Peel asparagus spears with a vegetable peeler from top to bottom, starting below the tips. Trim off any woody ends and chop asparagus spears, leaving the tips intact.
Bring a large pot of water to a boil. Add asparagus pieces, 1 tablespoon butter, sugar, and salt. Reduce heat; simmer until asparagus is tender and easily pierced with a knife, 15 to 25 minutes. Drain, reserving 2 cups cooking liquid.
Melt remaining 3 tablespoons butter in the pot. Cook shallots, stirring often, until translucent, about 5 minutes. Stir in flour until shallots are evenly coated. Whisk in reserved cooking liquid and white wine until soup is thick and smooth, about 5 minutes. Stir in Cambozola cheese until melted, about 1 minute.
Stir asparagus pieces, except for the tips, into the sauce. Add all but 2 teaspoons chervil leaves. Puree soup with an immersion blender until smooth. Season with salt and pepper.
Beat heavy cream in a bowl with an electric mixer until stiff peaks form. Stir cream into the soup. Garnish soup with reserved asparagus tips and 2 teaspoon chervil leaves.
